Generalized d’Alembert Formula for the Wave Equation with Discontinuous Coefficients

D. S. Anikonov; D. S. Konovalova

doi:10.1134/S0012266119020113

Generalized d’Alembert Formula for the Wave Equation with Discontinuous Coefficients

D. S. Anikonov, D. S. Konovalova

Кафедра дифференциальных уравнений ММФ

Результат исследования: Научные публикации в периодических изданиях › статья

Аннотация

We consider a second-order differential equation that is a mathematical model of transverse vibrations of a string or longitudinal vibrations of an elastic rod. The coefficients of the second derivatives are piecewise constant functions. An existence and uniqueness theorem is proved and an explicit formula is given for the generalized solution of the Cauchy problem.

Язык оригинала	английский
Страницы (с-по)	270-273
Число страниц	4
Журнал	Differential Equations
Том	55
Номер выпуска	2
DOI	https://doi.org/10.1134/S0012266119020113
Состояние	Опубликовано - 1 фев 2019

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Цитировать

Anikonov, D. S., & Konovalova, D. S. (2019). Generalized d’Alembert Formula for the Wave Equation with Discontinuous Coefficients. Differential Equations, 55(2), 270-273. https://doi.org/10.1134/S0012266119020113

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abstract = "We consider a second-order differential equation that is a mathematical model of transverse vibrations of a string or longitudinal vibrations of an elastic rod. The coefficients of the second derivatives are piecewise constant functions. An existence and uniqueness theorem is proved and an explicit formula is given for the generalized solution of the Cauchy problem.",

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N2 - We consider a second-order differential equation that is a mathematical model of transverse vibrations of a string or longitudinal vibrations of an elastic rod. The coefficients of the second derivatives are piecewise constant functions. An existence and uniqueness theorem is proved and an explicit formula is given for the generalized solution of the Cauchy problem.

AB - We consider a second-order differential equation that is a mathematical model of transverse vibrations of a string or longitudinal vibrations of an elastic rod. The coefficients of the second derivatives are piecewise constant functions. An existence and uniqueness theorem is proved and an explicit formula is given for the generalized solution of the Cauchy problem.

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Доступ к документу

10.1134/S0012266119020113

Link to publication in Scopus